LEADER 03701nam 2200529Ia 450 001 9910438151103321 005 20200520144314.0 010 $a1-4614-8118-X 024 7 $a10.1007/978-1-4614-8118-8 035 $a(OCoLC)859159256 035 $a(MiFhGG)GVRL6WKP 035 $a(CKB)2670000000530525 035 $a(MiAaPQ)EBC1398515 035 $a(EXLCZ)992670000000530525 100 $a20130817d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on sphere arrangements $ethe discrete geometric side /$fKaroly Bezdek 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (xii, 175 pages) $cillustrations (some color) 225 0 $aField Institute monographs,$x1069-5273 ;$vv. 32 300 $a"The thematic program on 'Discreet Geometry and Applications' took place at the Fields Institute for Research in Mathematical Sciences in Toronto between July 1 and December 31, 2011." 311 $a1-4614-8117-1 311 $a1-4939-0032-3 320 $aIncludes bibliographical references. 327 $a1. Unit Sphere Packings -- 2. Proofs on Unit Sphere Packings -- 3. Contractions of Sphere Arrangements -- 4. Proofs on Contractions of Sphere Arrangements -- 5. Ball-Polyhedra and Spindle Convex Bodies -- 6. Proofs on Ball-Polyhedra and Spindle Convex Bodies -- 7. Coverings by Cylinders -- 8. Proofs on Coverings by Cylinders -- 9. Research Problems - an Overview -- Glossary -- References. 330 $aThis monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers.  It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.   The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders.  . 410 0$aFields Institute monographs ;$vvolume 32. 606 $aDiscrete geometry$vCongresses 606 $aSphere packings$vCongresses 615 0$aDiscrete geometry 615 0$aSphere packings 676 $a516 676 $a516.11 676 $a516/.11 700 $aBezdek$b Karoly$01062468 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438151103321 996 $aLectures on sphere arrangements$93871527 997 $aUNINA